Insincere Equal Rankings

[Mike Ositoff]

On Thu, 25 Jun 1998, Hugh Tobin wrote:

> In January 1997 I posed the question for Condorcet [EM] advocates:
> 
> "What plausible set of expectations about the votes of others could I
> have that would give me a rational incentive, in Condorcet
> (margins-of-defeat), to truncate but not to reverse order?"

Of course you know that we discussed this at very great length in
'96, and I wrote many pages here about it. About the incentive to
not order-reverse. About the fact that Condorcet(EM) gives no reason
to truncate (unlike Young), except when truncation is used as
a defensive strategy when the offensive strategy of order-reversal
must be deterred. I hesitate to again write all that, but apparently
it will be necessary. My apologies to anyone who feels that I've
repeated those topics too much already. I'll get to that later in
this letter.

> 
> If there was an answer, I missed it.  If there is no answer, then one

But I can't believe that you missed it in '96.


> should not worry about the possible effects of "truncation" in Young's
> method. On the other hand, Markus has shown that in Condorcet [EM] there

Sure one should. Truncation, as I've explained till everyone was sick
of hearing it, will regularly happen without any offensive strategic
intent, regardless of the method. It's happened in every rank-balloting
election that I've participated in, including the one on EM.

Order-reversal, in contradistinction, is a consciously-intended
devious offensive strategy. As I showed at great length in '96, and
as I'll show again, it's well-deterred in Condorcet(EM). (Schulze
has the important properties of Smith//Condorcet(EM), in addition
to other desirable properties. The strategy statements I make about
Condorcet(EM) apply to Schulze).

> is an incentive for insincere equal rankings at the top of one's ballot
> (if one's preferences among favorites are weak compared to one's fear of

That's probably an inevitable result of a votes-against count. But
with Young, there's a need to do that in order to protect a likely
Condorcet winner against truncation (innocent or strategic). So actually
Young has that problem to a far more serious degree. And there can
be a need to actually rank a less-liked alternative _over_, not just
equal to, a more liked one, with Young, as a defemsive strategy to
protect a likely Condorcet winner from offensive strategy that would
otherwise elect someone you like less. Comparing something that could
conceivably be exploited in Condorcet as an offensive strategy, byk
an impossibly well-informed voter with a necessary defensive strategyk
in Young--not reasonable.

> the worst), and of course there is always an incentive in Condorcet
> [EM]for insincere random choices at the bottom, as between candidates
> about whom one knows nothing.  

Nonsense. Between candidates about whom one knows nothing, there's
no incentive to do anything but leave them all out, if they're all at
the bottom, as you said they are.
 
> IMHO, examples showing that "truncation" can be an effective insincere
> strategy under one tiebreak method but not another are not meaningful if
> both methods also allow a stronger insincere strategy in the same
> situation to achieve the same end -- for example, order-reversal by half

Yes, that's exactly what you said before, and what I answered then.

> as many voters as the number who would have needed to truncate in order
> to change the outcome under the first method.

Hugh's main point is that Condorcet(EM) doesn't offer an incentive
against order-reversal. Actually, with that method, order-reversal,
if its intended victims have any reason to expect it, is likely
to backfire, and result in a worse result for the reversers than the
one which would have occurred had they not reversed.

The defensive stategy, in Condorcet(EM), against order-reversal
is to not extend one's ranking any farther down than necessary.
This involves guessing about which alternative is Condorcet winner.
Amother possible defensive strategy would be to refuse to rank a
candidate if one believes that his voters are inclined to order-reverse.

If order-reversal were being organized on a scale sufficient to 
affect the outcome, it wouldn't be possible to keep it a secret from
its intended victims. They don't rank the order-reversers' candidates,
and the order-reversers are very sorry to have attempted that
offensive strategy. When based on intent to order-reverse, predictive
knowledge about who's Condorcet winner isn't even necessary. The
order-refersal cheating is deterred.

But say it's just a small (not public) election, in which order-reversers
can talk privately, or spontaneously be of like mind about it. Then
thers's no warning. The 1st time. In the following election, the
victims will remember what happened, and defensive truncation will
be applied to the party or candidate whose voters order-reversed before.

But suppose we're only talking about 1 election, so the intended
victimes really have no warning. No past history to go by. Small
non-public election where reversers can privately organize. Ok, then
it comes to guessing. The defenders have to guess who the Condorcet
winner is, and not rank any lower. But remember that their predictive
informatin is as good as that of the reversers. If the would-be
reversers know even that their intended victims _might_ not be
inclined to willingly set themselves up for slaughter by voting
for the candidates of those who want to cheat them, and that
defensive strategy might be used, and that the defenders have
access to the same polling information as the would-be reversers,
then they know that their order-reversal is likely to backfire.

Borrowing from others, I've likened this to a game of chicken,
in which the middle Condorcet winner's voters have much less to
lose than do the would-be reversers, even if they like the
reversers' candidate better than the one who'd win if theyk
punish the reversal. That's because, being in the middle, they're
not as far, as measured on the political spectrum, away from that
winner as the cheaters are.

Furthermore, the defenders have another advantage that defenders
always have: They're the ones who are in the right. Their threat
to stand on principle to deter cheating against them is more
credible than the would-be reversers' threat to produce the same
mutually undesirable result out of dishonest attempt to defeat
the rightful winner, the Condorcet winner. You're famililar with
that situation. The house cat defending its territory nearly always
chases the invading cat away, because the invader knows tht the
defending cat has greater motivation to engage in a fight that
could be damaging to both cats. That applies to human combatants
too. When I was in highschool I could have more of a Kamikaze
attitude toward a fight than an attacker, because he knew that
he had less reason to fight (also that he'd be the one who
couldn't claim self-defense later).

So, then, I've given lots of reasons why order-reversal is well-
deterred, under various conditions.

I should re-emphasize that, without order-reversal, Condorcet(EM)
has _no_ need for defensive strategy. No need to do other than
voting a complete & sincere ranking. That certainly can't be said
for Young, where ordinary innocent truncation can defeat a Condorcet
winner, & elect the truncators' candidate, and make you regret that
you didn't rank the Condorcet winner equal to your favorite.

I should file this order-reversal discussion, so that I won't always
have to repeat it.

At least I'll be able to refer people to the archives. 
For that matter, check out the '96 archives for the first go-around
where we covered exactly the same ground.

Mike



> 
> 
> -- Hugh Tobin
> 
>